Problem: What number could replace $a$ below? $\dfrac{2}{3} = \dfrac{6}{a}$
Solution: The fraction on the left represents 2 out of 3 slices of a rectangular pizza. How many total slices would we need if we want the same amount of pizza in 6 slices? We would need to cut the pizza into 9 slices. $\dfrac{2}{3} = \dfrac{6}{9}$ and so the answer is $9$ Another way to get the answer is to multiply by $\dfrac{3}{3}$ $\dfrac{3}{3} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{2}{3} \times \dfrac{3}{3} = \dfrac{6}{9} $ so our answer is $9$.